Advanced Augment Design

Advanced Design of Experiments: Augment 2-Level Factorial/Screening Design Dialog

In a foldover design, the signs of the selected factors are reversed so high becomes low (coded +1 -> -1) and low becomes high (coded -1 -> +1), and the new runs are added/augmented to the original design as a block. If the original design is Resolution III, and all factors are selected for foldover, the augmented design will be Resolution IV. In addition, the power of the design will improve with the foldover runs (a fold is treated as a replicate to estimate power using a main effects model).

If only one factor is selected, the new design will have that main effect free of any aliasing with two-way interactions and two-way interactions involving that factor will be free of aliasing with other two-way interactions, but the other factors will still have main effects aliased with two way interactions. This is useful for the case where the analysis of the initial design identifies a large main effect that is also expected to interact with other factors. This is effectively a hybrid Resolution III and V design. See Example 2: Advanced 2-Level Factorial/Screening Design with Augment - Foldover Design - BHH Bicycle.

If the original design is Resolution IV, and all factors are selected for foldover, the augmented design will still be Resolution IV, so this should not be used. On the other hand if only one factor is selected, then any two-way interactions involving that factor will be free of aliasing with other two-way interaction. If there are only four factors, selecting a single factor for foldover effectively creates a full-factorial design with two blocks.

Click Model Terms or Select All to select Factors to Fold. This will append the current design with those factors folded.

Include Blocks in Folded Runs — if there are blocks in the original design, the same number of blocks will be included in the folded runs, otherwise the folded runs are a single block.

Design Power Information — Terms in Model — select from One Main Effect, All Main Effects, ME + 2-Way Interactions or ME + All Interactions:
- Error degrees of freedom (df) = #Total Runs - #Specified Terms in Model - 1 (for constant).
- If Include Blocks in Mode and/or Include Center Points in the Model are checked, Error df is adjusted.
- If Error df is 0, an error message is given.
- If the specified number of terms exceeds the maximum permitted, only the maximum will be used.
- For formula details, see the Appendix: 2-Level Factorial/Screening Design — all calations.
Design Power Information — Number of Terms Omitted from Model — enter value, default is 0:
- Use this option to include all terms in the model when there are 3-Way Interactions or higher
- Error df = #Total Runs - (#Design Runs - #Terms Omitted from Model) - 1.
Design Power Information — Significance Level — enter alpha value, default is 0.05.

Randomize Folded Runs — check to randomize runs with Seed (Base) as either Clock or specified Value The latter will randomize the runs but always in the same random order for the same seed value. If unchecked, runs are in given in standard order.

Aliasing of Effects Report with Interactions to Order — enter value, default is 2.

Check Add Center Points to add specified number of center points. If there are categorical factors, all categorical combinations are included for each center point. If there are no continuous factors, the radio button for Add Center/Axial Points is greyed out.

Check Add Axial Points to add axial points. The default No. of Replicates will match the number of replicates in the factorial design. Note that the alpha value for a rotatable design will change if No. of Replicates is modified.

Select Alpha Axial Value as Rotatable, Face Centered or Custom. The formula for rotatable alpha axial value is given in the Appendix: Central Composite and Augment Design — Alpha Axial Value.

Randomize Center/Axial — check to randomize runs with Seed (Base) as either Clock or specified Value. The latter will randomize the runs but always in the same random order for the same seed value. If unchecked, runs are in given in standard order.

Fraction of Design Space (FDS) Plots For details on FDS Plots see the Appendix: Fraction of Design Space (FDS) Plots.

See Example 1: Advanced 2-Level Factorial/Screening Design with Augment — Add Axial Points — Cake Bake.

Include Blocks in Replicate Runs — if there are blocks in the original design, the same number of blocks will be included in the replicate runs, otherwise the replicate runs are a single block.

Design Power Information — Terms in Model — select from One Main Effect, All Main Effects, ME + 2-Way Interactions or ME + All Interactions:
- Error degrees of freedom (df) = #Total Runs - #Specified Terms in Model - 1 (for constant).
- If Include Blocks in Model and/or Include Center Points in the Model are checked, Error df is adjusted.
- If Error df is 0, an error message is given.
- If the specified number of terms exceeds the maximum permitted, only the maximum will be used.
- For formula details, see the Appendix: 2-Level Factorial/Screening Design — Power Calculations.

Design Power Information — Number of Terms Omitted from Model — enter value, default is 0:
- Use this option to include all terms in the model when there are 3-Way Interactions or higher.
- Error df = #Total Runs - (#Design Runs - #Terms Omitted from Model) - 1.

Design Power Information — Significance Level — enter alpha value, default is 0.05.

Randomize Replicate Runs — check to randomize runs with Seed (Base) as either Clock or specified Value. The latter will randomize the runs but always in the same random order for the same seed value. If unchecked, runs are in given in standard order.